The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  1
 0  X  0  0 2X 2X^2+X  X 2X 2X^2+2X 2X^2+X  X 2X^2+X  0
 0  0  X 2X  0 2X^2+2X  X 2X 2X^2+X 2X^2+2X  X  0 X^2
 0  0  0 X^2  0 2X^2  0 X^2  0 2X^2 2X^2 X^2 2X^2
 0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 2X^2

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+34x^18+114x^19+54x^20+250x^21+642x^22+324x^23+2596x^24+1602x^25+6480x^26+4648x^27+1704x^28+432x^29+452x^30+312x^31+32x^33+6x^36

The gray image is a linear code over GF(3) with n=117, k=9 and d=54.
This code was found by Heurico 1.16 in 0.194 seconds.